**2. Numerical Method**

Figure 1 shows the simulation set-up, which consists of an annulus region formed by two concentric horizontal hexagonal cylinders of di fferent sizes, considered in the present work. Simulations are performed inside a square enclosure and 251×251 lattice grid points are used to divide the computational domain. The center positions of the two hexagonal cylinders are fixed at the center of the enclosure. *Lout* in the figure represents the distance between two opposite sides of the outer hexagonal cylinder (the size of the outer cylinder). Throughout the simulations, *Lout* is kept constant at *Lout* = 212 and the size for the inner hexagonal cylinder, *Lin* in Figure 1, is varied based on the aspect ratio, which is defined as: AR = *Lin*/*Lout*. *g* in the figure denotes the gravitational acceleration constant.

**Figure 1.** Simulation set-up for investigating the natural convection in an annulus region between two concentric hexagonal cylinders. The origin of the lattice grid is mentioned by ' *O*' in the figure.

The initial values for the fluid velocity and temperature inside the domain are set to zero. The no-slip and constant temperature BC ( *To* = *Tc* ≡ 0) are applied at the enclosure walls for the flow field and temperature field, respectively, and the standard mid-plane BB scheme is used to treat the

no-slip boundary condition. The temperature value for all edges/sides of the outer hexagonal cylinder is kept constant at, *Tout* ≡ *Tc* = 0 (cold surface), and that for the inner one is fixed at *Tin* ≡ *Th* = 1 (hot surface). The constant temperature and no-slip BC on all sides of the inner and outer cylinder are treated with SPM. In below, the formulations for LBM for solving the fluid flow field, FDM for solving the temperature field, and SPM for treating BC on hexagonal edges are provided.
